Tasks: 1. Design two algorithms in pseudocode: one for the insert operation and the other for the removeMin operation, both for a Heap implemented on an array H. 2. Using your favorite programming language, implement the Heap ADT on an array, in the following operations: insert, removeMin, min, size and isEmpty. Use the insert and removeMin algorithms of #1 3, Design the Heap-Sort algorithmn in pseudocode, which uses the Heap ADT of #2. Your algorithm should sort an array of integers in increasing order designed in #3. O-notatio favorite programming language, implement the Heap-Sort algorithm you 5. What are the worst and best-case time complexities of Insert, removeMin, and Heap-Sort, in n? Why? Your answer must be based on the algorithms you implemented. 6. Generate an array A of n random integers. Sort array A using Insertion-Sort, Quicksort, and Heap-Sort. Do this for arrays of size n 10, 100, 1000, 10000, 100000, 100000. Keep track of the CPU time each algorithm takes to sort these arrays. Comment on the running times you obtained, and compare them to the complexities as discussed in class. Hint: place the CPU times you obtained in a table